If the US dollar were to depreciate versus the currency of other countries it trades with, it means that a larger number of dollars can be procured with the same number of units of any other country's currency. Goods and services exported by any country are marked in terms of its currency. A depreciation in the currency would make it easier for US exporters to sell their products to other countries as they would be less expensive for the buyers. This would benefit the portion of the economy that is reliant on export and improve the balance of trade.
On the other hand, a depreciation in the dollar would decrease the number of units of another country's currency that can be bought with the same number of dollars and this would make products imported from other countries more expensive. For example, a fall in the value of the dollar versus the currency of any country that the US imports oil from would increase the cost of gasoline sold in the US. As the costs of imports increases, it could lead to inflation that would reduce the benefits incurred from the increased inflow of funds due to exports.